To some this might be a contradiction in terms. Some people live their lives defined by events, by structural and societal norms and expectations, and through the lens of ‘this is meant to be because this is what happens’. Some might see this as an overwhelming and daunting task that continues lifelong and can never actually be achieved. Those that do not see this as a contradiction, but as a challenge and a life path sometimes choose to focus only on the positive. They look at what “I am” and strive to improve on those qualities and others which have not yet been achieved and to dodge the negative events that occur, somewhat like a rabbit going through life blissful and beautiful and sweet until having to race in terror from the eagle/fox/dog/cat that is attempting to catch and kill and eat it.
So, for clarity, I don’t find defining oneself as a contradiction in terms, but one of the main purposes of life. If we can’t take our toys with us when we go, if we’re here for a purpose(s) then one of them is for soul growth. And part of growth is to come into a clearer, wiser, broader sense of the self. Part of this is learning from the things that happen to us. ‘Shit happens’ is very true. We are part of an infinitely interrelated ecosystem of which we are not fully in control. So we are just as much players on other people’s stage as they are players for us. But we also have free will and the agency to take action in our lives. We are in control of ourselves and so can choose what we do and how we do it within the ‘shit happens’ of the world around us. So I agree with those who want to focus on the positive and enhance it in their lives. But I think solely focusing on that is missing a key component for balance and true growth.
To define ourselves we need to look not just at what we currently are and what we aspire to be, but what we are not. Because part of this life is creating a life that is positive and that means learning what is not positive and creating boundaries for ourselves that helps us keep those actions/thoughts/choices from occurring or reoccurring. It’s not about looking at the obvious like ‘I’m not a brain surgeon’ or ‘I’m not a nuclear physicist’ but looking at what you have experienced and have chosen to no longer participate in/with in your life. So the statement is more ‘I am no longer…..’ . I’m sure we all can fill in quite a few of those blanks fairly easily: a binge drinker, a gambler, codependant, a member of a discriminatory organization, living someone else’s expectations, fulfilling the role my family/religion/culture bequeathed to me…the list goes on and on and on.
The thing is, to define ourselves by what we are not, we have to leave the comforting place of everything that is right and look at what has not fit, done damage, hurt us deeply, left us disillusioned and see that it is no longer so. It takes courage just to look at those things, to do that final tally and find that it is true that they are no longer us. We are not that. What takes even more courage is that looking at these things brings into focus those things that are still us, but no longer should be. Those things that are not pretty, that are still living in the shadows, that keep telling us ‘you can’t deal with me, not yet’ and that in the end keep the good things from fully actuating. It takes courage because once you see 
them, you can’t unsee them. It takes a tremendous act of will to forget them or push them away. And if you are truly seeking a balanced, authentic definition of self, it’s not something you can do. You have to look at these things. With a bright spotlight. With the full light of day. And get ready to do what it takes to say NO! To say “I’m not that” and have that be real. That’s where the true magic begins. When you slay the dragon, as Joseph Campbell has put it, and are able to walk past it to your real self.